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Re: Terminating Deciamal Expansion
Posted:
Jan 19, 2013 1:15 PM


"Virgil" <virgil@ligriv.com> wrote in message news:virgilB385CE.21472618012013@BIGNEWS.USENETMONSTER.COM... > In article <1oCdneKuT4nqi2fNnZ2dnUVZ_rCdnZ2d@earthlink.com>, > "Charles Hottel" <chottel@earthlink.net> wrote: > >> I would appreciate some hints on solving this problem: >> >> Show that any rational number p/q, for which the prime factorization of q >> consists entirely od 2s and 5s, has a terminating decimal expansion. >> Thanks. > > If q = 2^m*5^n for nonnegative integers m and n, let k = max(m,n) > > then r = (p/q)*10^k is an integer, so and p/q = r/10^k. >  > > Thanks I see it now.



